It is generally acknowledged that the mass-loss of asymptotic giant branch (AGB) stars undergoes variations on different time-scales. We constructed models for the dust envelopes for a sample of AGB stars to assess whether mass-loss variations influence the spectral energy distribution. To constrain the variability, extra observations at millimetre wavelengths (1.2 mm) were acquired. From the analysis of the dust models, two indications for the presence of mass-loss variations can be found, being (1) a dust temperature at the inner boundary of the dust envelope that is far below the dust condensation temperature and (2) an altered density distribution with respect to rho(r) proportional to r(-2) resulting from a constant mass-loss rate. For five out of the 18 studied sources a two-component model of the envelope is required, consisting of an inner region with a constant mass-loss rate and an outer region with a less steep density distribution. For one source an outer region with a steeper density distribution was found. Moreover, in a search for time variability in our data set at 1.2 mm, we found that WX Psc shows a large relative time variation of 34 per cent which might partially be caused by variable molecular line emission.